Hypergeometric and Generalized Hypergeometric Group Testing

We consider two group testing problems involving a set of n items. In the first problem extactlyd defectives, and in the second problem at mostd defectives, are distributed arbitrarily in the set. We show that any procedure for identifying all defectives in the first problem can be easily adapted to the second problem, with an increase of at most one in the maximum number of tests required. Some related problems are also described.